#include<iostream>
#include<vector>
#include<queue>
#include<cstring>
#include<cmath>
#include<map>
#include<set>
#include<cstdio>
#include<algorithm>
#define debug(a) cout<<#a<<"="<<a<<endl;
using namespace std;
const int maxn=2e5+1000;
typedef long long LL;
inline LL read(){LL x=0,f=1;char ch=getchar();	while (!isdigit(ch)){if (ch=='-') f=-1;ch=getchar();}while (isdigit(ch)){x=x*10+ch-48;ch=getchar();}
return x*f;}
int main(void){
   	cin.tie(0);std::ios::sync_with_stdio(false);
    LL t;cin>>t;
    while(t--){
        LL n,m,k;cin>>n>>m>>k;
        if(n%2==0&&m%2==0){
            if(k%2==0){
                cout<<"YES"<<"\n";
            }
            else{
                cout<<"NO"<<"\n";
            }
        }
        else if(n%2==0&&m%2!=0){
            if(k<=n*m/2-n/2&&k%2==0){
                cout<<"YES"<<"\n";
            }
            else{
                cout<<"NO"<<"\n";
            }
        }
        else if(n%2!=0&&m%2==0){
            if(k>=m/2){
                k-=m/2;
                if(k&1) cout<<"NO"<<"\n";
                else cout<<"YES"<<"\n";
            }
            else{
                cout<<"NO"<<"\n";
            }
        }
    }
   	return 0;
}
